1/N 2 corrections to the holographic Weyl anomaly

108

207

We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology S 1 × S D−1 is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.

Section: 4)mentioning

confidence: 99%

“…where 10) and , denotes the canonical pairing between a Cartan subalgebra and its dual. In a consistent theory, there are no cubic or mixed 't Hooft anomalies for the gauge symmetry G, meaning that the total contribution E = E vm +E cm is independent of the gauge chemical potential z.…”

Section: Jhep09(2015)142mentioning

confidence: 99%

Supersymmetric Casimir energy and the anomaly polynomial

Bobev

Bullimore

Kim

2015

108

207

“…The combination c − a plays an important role in holographic theories [77], and it would be worth exploring if there is a connection. Formulas for c − a in terms of short multiplets in the bulk have appeared in [26,27,78].…”

Section: Jhep04(2017)055mentioning

confidence: 99%

“…To see whether Re(V eff M 3 (a = 0)) = 0 is a local minimum or maximum, we again compute the quantity 27) as in the cases M 3 = L(n, 1) and S 1 × Σ g . In the region of |α · x| < 1 and |ρ I · x| < 1 for every ρ I , we can easily calculate this as…”

Section: Jhep04(2017)055mentioning

confidence: 99%

“…Similarly to the Cardy formula in 2d CFT [24], this limit controls the asymptotic behavior at large energies of the weighted density of short states. Following the observations in [25][26][27], and assuming the existence of a weakly-coupled point in the space of couplings, 1 it was argued in [28] that for β → 0 the partition function has a universal behavior (see also [34][35][36][37][38])…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cardy formula for 4d SUSY theories and localization

Pietro

Honda

2017

119

Abstract:We study 4d N = 1 supersymmetric theories on a compact Euclidean manifold of the form S 1 × M 3 . Partition functions of gauge theories on this background can be computed using localization, and explicit formulas have been derived for different choices of the compact manifold M 3 . Taking the limit of shrinking S 1 , we present a general formula for the limit of the localization integrand, derived by simple effective theory considerations, generalizing the result of [1]. The limit is given in terms of an effective potential for the holonomies around the S 1 , whose minima determine the asymptotic behavior of the partition function. If the potential is minimized in the origin, where it vanishes, the partition function has a Cardy-like behavior fixed by Tr(R), while a nontrivial minimum gives a shift in the coefficient. In all the examples that we consider, the origin is a minimum if Tr(R) ≤ 0.

One-loop holographic Weyl anomaly in six dimensions

Liu

McPeak

2018

Self Cite

We compute O(1) corrections to the holographic Weyl anomaly for sixdimensional N = (1, 0) and (2, 0) theories using the functional Schrödinger method that is conjectured to work for supersymmetric theories on Ricci-flat backgrounds. We show that these corrections vanish for long representations of the N = (1, 0) theory, and we obtain an expression for δ(c − a) for short representations with maximum spin two. We also confirm that the one-loop corrections to the N = (2, 0) M5-brane theory are equal and opposite to the anomaly for the free tensor multiplet. Finally, we discuss the possibility of extending the results to encompass multiplets with spins greater than two.